An Extreme Value Theory Approach to Calculating Minimum Capital Risk Requirements

Posted: 4 Dec 2004

See all articles by Chris Brooks

Chris Brooks

University of Reading - ICMA Centre

Andrew Clare

City University London - Sir John Cass Business School

Gita Persand

University of Bristol - Department of Economics

Abstract

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semi-parametric approach where the tails are modelled by the Generalized Pareto Distribution and smaller risks are captured by the empirical distribution function. We compare the capital requirements form this approach with those calculated from the unconditional density and from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample and for a hold-out sample, our extreme value approach yields superior results than either of the other two models which do not explicitly model the tails of the return distribution. Since the use of these internal models will be permitted under the EC-CAD II, they could be widely adopted in the near future for determining capital adequacies. Hence, close scrutiny of competing models is required to avoid a potentially costly misallocation capital resources while at the same time ensuring the safety of the financial system.

Keywords: Minimum Capital Risk Requirements, Generalized Pareto Distribution, GARCH models

JEL Classification: C14, C15, G13

Suggested Citation

Brooks, Chris and Clare, Andrew D. and Persand, Gita, An Extreme Value Theory Approach to Calculating Minimum Capital Risk Requirements. Journal of Risk Finance, Vol. 3, No. 2, pp. 22-33, 2002; Cass Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=626692

Chris Brooks (Contact Author)

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading RG6 6BA
United Kingdom
+44 118 931 82 39 (Phone)
+44 118 931 47 41 (Fax)

Andrew D. Clare

City University London - Sir John Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Gita Persand

University of Bristol - Department of Economics ( email )

8 Woodland Road
Bristol BS8 ITN
United Kingdom

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